The classical definition of degrees of freedom (DoF) deals with the degree of a communication channel or multiple communication channels at the limit of high SNR. This can be interpreted as the number of independent streams that can be sent in each communication channel at high SNR regime.
Consider a point to point channel between a transmitter and a receiver both equipped with multiple antennas. It is well known that for independent Gaussian channel model between each pair of transmit and receive antennas the capacity of the corresponding multiple antenna input and multiple antenna output (MIMO) channel scales with the minimum of the number of antennas at the transmitter (NT) and the receiver (NR) at the limit of high SNR. The degrees of the freedom of the channel is then defined as the quantity min(NT,NR). The concept of degree of freedom may also be interpreted as the possibility or measure of the number of independent streams that can be transmitted simultaneously in the channel. It is immediate to see the usefulness of extending this concept in multiuser networks where we are interested to understand the number of simultaneous streams that can be transmitted between different transmit and receiver subset of the nodes in the network. For example, degrees of freedom in a three user interference channel with N antennas at each node is defined similarly as the scaling of the channel capacity between each pair of the users as a function of log(SNR). The same concept may be extended to define the three tuple d=(d1,d2,d3) that can be achieved simultaneously, where di denotes the scaling of the channel capacity between the ith transmitter and receiver pair. While there may be multiple choices of d achievable in this network the region of all such d defines the available degrees of freedom region.